Some modifications of paracompactness (Q2765949)
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scientific article; zbMATH DE number 1695213
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some modifications of paracompactness |
scientific article; zbMATH DE number 1695213 |
Statements
19 February 2003
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\(P_1\)-metacompact
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\(P_1\)-paracompact
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\(\omega^*\)-paracompact
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Some modifications of paracompactness (English)
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A topological space \(X\) is called \(P_1\)-metacompact (resp. \(P_2\)-metacompact) if every preopen cover has a point-finite open (resp. preopen) indexed refinement. The author considers these notions and compares them to the notions of \(P_1\)-paracompact (resp. \(P_2\)-paracompact) spaces investigated by the reviewer and I. Reilly. In addition, the concept of an \(\omega^*\)-paracompact space is studied, where the space is said to be \(\omega^*\)-paracompact if every \(\omega\)-open cover has a locally finite \(\omega\)-open refinement.
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